An elastic body of this type can comprise any body, which exhibits, under action of a force or a pressure, a reversible deflection from its equilibrium position. An example of such a body is a ceramic measuring membrane, or diaphragm, of a pressure sensor. A pressure sensor having such a measuring membrane is disclosed, for example, in German Published Application Offenlegungsschrift DE 39 12 217. Such pressure sensors are applied frequently in process measurements applications, wherein the measuring membranes are, not seldomly, subjected to corrosive media. The measuring membrane of DE 39 12 217 includes, as a base material, an aluminum oxide ceramic or silicon, wherein at least the media-side surface of the measuring membrane has a protective layer of silicon carbide, in order to increase its corrosion resistance as an isolating membrane. This protective layer is prepared by means of a plasma supported chemical gas phase deposition (PECVD, for the English, Plasma Enhanced Chemical Vapor Deposition). To the extent, however, that the surfaces of the base material have significant roughness, the SiC layers prepared by means of PECVD on these substrates have a relatively large defect density, so that, while having an improved corrosion resistance compared with uncoated membranes, their corrosion resistance still leaves something to be desired.